SIGMA: A Sigmoid-Gated Sampler for Test-Time Scaling in Diffusion Language Models

Autoregressive language models generate under a fixed left-to-right order, whereas diffusion language models (dLLMs) denoise masked tokens through flexible any-order trajectories that may commit multiple positions per step. This makes dLLMs a distinctive setting for test-time scaling: additional inference compute can diversify both token choices and the order in which positions are committed. Existing samplers do not explicitly allocate these two sources of diversity. Confidence-based decoding is reliable but often redundant, while global temperature sampling and random remasking inject stochasticity without distinguishing useful exploration from unreliable commitments. We propose SIGMA, a training-free sampler that formulates each denoising step as a constrained allocation problem over decoding efficiency, token-level diversity, trajectory-level diversity, and model-internal commitment uncertainty. The resulting objective decomposes joint sampling entropy into token and trajectory terms, yielding a sigmoid-form stochastic gate for position selection and an adaptive per-position temperature for token sampling. Experiments on LLaDA and Dream across math and code benchmarks show that SIGMA improves the accuracy–cost Pareto frontier and can be integrated into existing dLLM test-time scaling pipelines.